Deutsch

Definition

A comma is a small interval that occurs in just intonation, between two intervals which are close in pitch. Commas are always greater than 1 and not a power such as a square or cube of any other interval, and generally in a low prime limit. The word is often used in reference to regular tempering when the comma is tempered out, which is to say reduced to a unison, by the temperament, thereby equating the intervals separated by that comma. For example the Syntonic or Didymus comma of 81/80, which occurs between 10/9 and 9/8, as well as 81/64 and 5/4, is tempered out by meantone temperament. Commas are usually written as ratios, but they can also be written as monzos. The following lists mostly give both forms, as well as the size in cents.

For commas over 100 cents in size, see Large commas; and for commas under 3.5 cents in size, see Unnoticeable commas

List of commas, by prime limit

3-limit commas

name(s)	ratio	monzo	cents
limma, Pythagorean minor second	256 / 243	| 8 -5 >	90.225
Pythagorean comma		| -19 12 >	23.460
17-comma		| 27 -17 >	66.765
29-comma		| 46 -29 >	43.305
41-comma		| 65 -41 >	19.845
Pythagorean Integer cents comma		| 317 -200 >	9.000
Mercator's comma, 53-comma		| -84 53 >	3.615
70-comma		| 111 -70 >	63.150

5-limit commas

name(s)	ratio	monzo	cents
Twenty-two thirds limma		| -51 0 22 >	98.902
sibbolet		| -58 0 25 >	57.843
Hunt 5-cycle comma		| -65 0 28 >	16.784
acute thirds comma		| 72 0 -31 >	24.275
34-5-comma		| 79 0 -34 >	65.334
Schismic thirds chromatic semitone		| -123 0 53 >	74.627
10-15-comma		| -39 10 10 >	82.687
11-15-comma		| 43 -11 -11 >	29.044
21-15-comma		| 82 -21 -21 >	53.643
32-15-comma		| 125 -32 -32 >	24.599
Huntian 15-cycle comma		| -168 43 43 >	4.445
53-15-comma		| -207 53 53 >	78.242
54-15-comma		| 211 -54 -54 >	33.489
76-15-comma		| 297 -76 -76 >	91.578
major chroma, major limma, pelogic comma	135 / 128	| -7 3 1 >	92.179
ripple	6561 / 6250	| -1 8 -5 >	84.071
doublewide		| -9 -6 8 >	78.780
sevond		| 6 -14 7 >	76.826
nusecond		| 5 13 -11 >	75.964
sentinel		| -33 15 4 >	74.580
chromatic semitone	25 / 24	| -3 -1 2 >	70.672
superpyth, grave minor second	20480 / 19683	| 12 -9 1 >	68.719
major diesis, diminished comma	648 / 625	| 3 4 -4 >	62.565
passion		| 18 -4 -5 >	60.611
shibboleth		| -5 -10 9 >	57.273
mynic		| 9 9 -10 >	54.458
tritonic		| -29 11 5 >	53.074
negri comma, double augmentation diesis	16875 / 16384	| -14 3 4 >	51.120
maximal diesis, porcupine comma	250 / 243	| 1 -5 3 >	49.166
immunity		| 16 -13 2 >	47.212
diesis, augmented comma	128 / 125	| 7 0 -3 >	41.059
wizard		| -31 2 12 >	39.675
sycamore		| -16 -6 11 >	37.721
fifive		| -1 -14 10 >	35.767
unicorn		| -2 13 -8 >	34.905
valensixthtone		| 13 5 -9 >	32.952
ampersand, Ampersand's comma		| -25 7 6 >	31.567
small diesis, magic comma	3125 / 3072	| -10 -1 5 >	29.614
minimal diesis, tetracot comma	20000 / 19683	| 5 -9 4 >	27.660
roda		| 20 -17 3 >	25.706
maja		| -3 -23 17 >	22.368
syntonic comma, Didymos comma, meantone comma	81 / 80	| -4 4 -1 >	21.506
maquila comma		| 49 -6 -17 >	20.937
diaschisma	2048 / 2025	| 11 -4 -2 >	19.553
ditonma		| -27 -2 13 >	18.168
misty comma		| 26 -12 -3 >	17.599
pental comma		| -28 25 -5 >	17.306
graviton, gravity comma		| -13 17 -6 >	15.353
quartonic		| 3 -18 11 >	14.261
medium semicomma, sensipent comma	78732 / 78125	| 2 9 -7 >	13.399
Würschmidt comma		| 17 1 -8 >	11.445
semicomma, Fokker comma		| -21 3 7 >	10.061
escapade comma		| 32 -7 -9 >	9.492
kleisma, semicomma majeur	15625 / 15552	| -6 -5 6 >	8.107
unidecma		| -7 22 -12 >	7.245
mutt comma		| -44 -3 21 >	6.723
amity comma		| 9 -13 5 >	6.154
parakleisma		| 8 14 -13 >	5.292
gammic comma		| -29 -11 20 >	4.769
vulture comma		| 24 -21 4 >	4.200
23-3/5-comma		| 17 23 -23 >	59.750
34-3/5-comma		| -25 -34 34 >	68.196
53-3/5-comma		| 39 53 -53 >	71.012

7-limit commas

name(s)	ratio	monzo	cents
hexadecatone comma, 16-7-comma		| 45 0 0 -16 >	98.7855
21-7-comma		| 59 0 0 -21 >	54.656
Hunt 7-cycle comma		| 73 0 0 -26 >	10.526
German sixth comma		| -87 0 0 31 >	33.603
large deep red comma	6561 / 6272	| -7, 8, 0 -2 >	77.988
36-7-comma		| -101 0 0 36 >	77.737
47-7-comma		| 132 0 0 0 -47 >	65.182
slendro integer cents comma		| 1127 0 0 -400 >	69.637
29-7/5-comma		| -14 0 -29 29 >	92.854
31-7/5-comma		| -15 0 -31 31 >	57.878
33-7/5-comma		| -16 0 -33 33 >	22.902
35-7/5-comma		| 18 0 35 -35 >	12.073
37-7/5-comma		| 19 0 37 -37 >	47.049
39-7/5-comma		| 20 0 39 -39 >	82.0245
5-21-comma		| 22 -5 0 -5 >	46.0955
18-21-comma		| -79 18 0 18 >	74.056
23-21-comma		| -101 23 0 23 >	27.961
Huntian 21-cycle comma		| 123 -28 0 -28 >	18.135
33-21-comma		| 145 -33 0 -33 >	64.230
8-35-comma		| -41 0 8 8 >	41.117
15-35-comma		| 77 0 -15 -15 >	72.906
23-35-comma		| 118 0 -23 -23 >	31.789
31-35-comma		| -159 0 31 31 >	9.328
39-35-comma		| -200 0 39 39 >	50.445
47-35-comma		| -241 0 47 47 >	91.562
Huntian 35-cycle comma		| 277 0 -54 -54 >	22.4605
greenwoodma	405 / 392	| -3 4 1 -2 >	56.482
Harrison's comma	59049 / 57344	| -13 10 0 -1 >	50.724
keega	1029 / 1000	| -3 1 -3 3 >	49.492
septimal quarter tone	36 / 35	| 2 2 -1 -1 >	48.770
quarter tone comma		| 49 50 -25 -25 >	19.2595
cloudy	16807 / 16384	| -14 0 0 5 >	44.130
Avicenna, Avicenna's enharmonic diesis	525 / 512	| -9 1 2 1 >	43.408
slendro diesis	49 / 48	| -4 -1 0 2 >	35.597
slendro 34-comma		| -137 -34 0 68 >	13.692
34-jubilismic comma		| -33 0 -68 68 >	10.829
tritonic diesis, jubilisma	50 / 49	| 1 0 2 -2 >	34.976
eric		| 7 8 0 -7 >	33.859
senga	686 / 675	| 1 -3 -2 3 >	27.985
septimal comma, Archytas' comma, Leipziger Komma	64 / 63	| 6 -2 0 -1 >	27.264
blackjackisma		| -10 7 8 -7 >	22.413
squalentine	64827 / 64000	| -9 3 -3 4 >	22.227
keema	875 / 864	| -5 -3 3 1 >	21.902
gariboh	3125 / 3087	| 0 -2 5 -3 >	21.181
nuwell	2430 / 2401	| 1 5 1 -4 >	20.785
tolerma		| 10 -11 2 1 >	19.948
mirwomo	33075 / 32768	| -15 3 2 2 >	16.144
trimyna	50421 / 50000	| -4 1 -5 5 >	14.516
sensamagic	245 / 243	| 0 -5 1 2 >	14.191
septimal semicomma, starling comma	126 / 125	| 1 2 -3 1 >	13.795
octagar	4000 / 3969	| 5 -4 3 -2 >	13.469
orwellisma, orwell comma	1728 / 1715	| 6 3 -1 -3 >	13.074
quince		| -15 0 -2 7 >	9.154
gamelisma	1029 / 1024	| -10 1 0 3 >	8.433
varunisma		| -9 8 -4 2 >	8.037
septimal kleisma, marvel comma	225 / 224	| -5 2 2 -1 >	7.712
dimcomp		| -1 -4 8 -4 >	7.386
cataharry	19683 / 19600	| -4 9 -2 -2 >	7.316
mirkwai	16875 / 16807	| 0 3 4 -5 >	6.990
stearnsma		| 1 10 0 -6 >	6.595
hemimage	10976 / 10935	| 5 -7 -1 3 >	6.479
hemimean	3136 / 3125	| 6 0 -5 2 >	6.083
hemifamity	5120 / 5103	| 10 -6 1 -1 >	5.758
linus		| 11 -10 -10 10 >	5.572
porwell	6144 / 6125	| 11 1 -3 -2 >	5.362
garischisma		| 25 -14 0 -1 >	3.804
wadisma		| -26 -1 1 9 >	3.792
quasiorwellisma		| 22 -1 -10 1 >	3.734
218edo (stacked 7/4 and 10/9) comma		| 22 -32 16 -3 >	11.982
bapbo	256 / 245	| 8 0 -1 -2 >	76.034

11-limit commas

name(s)	ratio	monzo	cents
11-cycle chroma, 11-11-comma		| -38 0 0 0 11 >	64.497
11-cycle major seventh prote, 35-11-comma		| -121 0 0 0 35 >	96.128
Hunt 11-cycle comma		| -83 0 0 0 24 >	31.631
Hunt flat 5 comma	8192 / 8019	| 13 -6 0 0 -1 >	36.952
sterno	352 / 343	| 5 0 0 -3 1 >	44.840
the Igs boson, 13-11-comma		| 45 0 0 0 -13 >	32.867
telepathma	55 / 54	| -1 -3 1 0 1 >	31.767
thuja comma		| 15 0 1 0 -5 >	29.724
sensmus	1232 / 1215	| 4 -5 -1 1 1 >	24.055
sevnothrush	3168 / 3125	| 5 2 -5 0 1 >	23.659
cassacot	245 / 242	| -1 0 1 2 -2 >	21.330
mothwellsma	99 / 98	| -1 2 0 -2 1 >	17.576
ptolemisma	100 / 99	| 2 -2 2 0 -1 >	17.399
hemimin	1344 / 1331	| 6 1 0 1 -3 >	16.827
biyatisma	121 / 120	| -3 -1 -1 0 2 >	14.367
aphrowe	1331 / 1323	| 0 -3 0 -2 3 >	10.437
valinorsma	176 / 175	| 4 0 -2 -1 1 >	9.865
pentacircle	896 / 891	| 7 -4 0 1 -1 >	9.688
orgonisma	65536 / 65219	| 16 0 0 -2 -3 >	8.394
rastma	243 / 242	| -1 5 0 0 -2 >	7.139
myhemiwell	3388 / 3375	| 2 -3 -3 1 2 >	6.656
keenanisma	385 / 384	| -7 -1 1 1 1 >	4.503
werckisma	441 / 440	| -3 2 -1 2 -1 >	3.930
moctdel	1375 / 1372	| -2 0 3 -3 1 >	3.781

13-limit commas

name(s)	ratio	monzo	cents
Hunt 13-cycle comma		| -37 0 0 0 0 0 10 >	5.277
silver half cents comma		| -8881 0 0 0 2400 >	66.389
Hunt minor submediant comma	1053 / 1024	| -10 4 0 0 0 0 1 >	48.348
astburyp		| -19 -2 0 0 0 6 >	39.255
wilsorma	65 / 64	| -6 0 1 0 0 1 >	26.841
winmeanma	66 / 65	| 1 1 -1 0 1 -1 >	26.432
negustma	78 / 77	| 1 1 0 -1 -1 1 >	22.229
superleap	91 / 90	| -1 -2 -1 1 0 1 >	19.130
animist	105 / 104	| -3 1 1 1 0 -1 >	16.567
secorian	28672 / 28431	| 12 -7 0 1 0 -1 >	14.613
mosaic	3159 / 3136	|-6 5 0 -2 0 1>	12.651
gassorma	275 / 273	| 0 -1 2 -1 1 -1 >	12.637
grossma	144 / 143	| 4 2 0 0 -1 -1 >	12.064
buzurgisma, dhanvantarisma	169 / 168	| -3 -1 0 -1 0 2 >	10.274
catadictma	1287 / 1280	| -8 2 -1 0 1 1 >	9.442
mynucuma	196 / 195	| 2 -1 -1 2 0 -1 >	8.855
huntma	640 / 637	| 7 0 1 -2 0 -1 >	8.134
threedie	2197 / 2187	| 0 -7 0 0 0 3 >	7.897
kestrel comma	1188 / 1183	| 2 3 0 -1 1 -2 >	7.302
marveltwin	325 / 324	| -2 -4 2 0 0 1 >	5.335
ratwolfsma	351 / 350	| -1 3 -2 -1 0 1 >	4.939
minthma	352 / 351	| 5 -3 0 0 1 -1 >	4.925
gentle comma	364 / 363	| 2 -1 0 1 -2 1 >	4.763
cuthbert	847 / 845	| 0 0 -1 1 2 -2 >	4.093

17-limit commas

name(s)	ratio	monzo	cents
11 semitone comma		| 45 0 0 0 0 0 -11 >	45.4905
12 semitone comma		| -49 0 0 0 0 0 12 >	59.465
23 semitone comma		| -93 0 0 0 0 0 23 >	13.974
Hunt 17-cycle comma		| -138 0 0 0 0 0 34 >	31.516
17-ripple integer cents comma		| 327 0 0 0 0 0 -80 >	3.568
Hunt flat 2 comma	4131 / 4096	| -12 5 0 0 0 0 1 >	14.730
Blume comma	2057 / 2048	| -11 0 0 0 2 0 1 >	7.591
Septendecimal Integer Cents comma	289 / 288	| -5 -2 0 0 0 0 2 >	6.001
Tannisma	273/272	|-4 1 0 1 0 1 -2>	6.353

19-limit commas

name(s)	ratio	monzo	cents
Hunt 19-cycle comma		| 17 0 0 0 0 0 0 -4 >	9.950
spleen comma	210 / 209	| 1 1 1 1 -1 0 0 -1 >	8.264
go comma	361 / 360	| -3 -2 -1 0 0 0 0 2 >	4.802